I understand that with simple linear regression, each estimated coefficient has an associated p-value that corresponds to the null hypothesis that the coefficient in question is 0. If this p-value is less than some significance level, then we reject that null hypothesis.
Does the same thing hold for results coming from a VAR model used to fit multivariate time series data? For example, I'm looking at this output from statsmodels:
Results for equation Y
=============================================================================================================
coefficient std. error t-stat prob
-------------------------------------------------------------------------------------------------------------
const -137462.630878 2366245.152723 -0.058 0.954
L1.Y -0.627474 0.063546 -9.874 0.000
L1.X -708.839187 2858.506570 -0.248 0.804
=============================================================================================================
How do I interpret those prob values? Is the hypothesis the same as for linear regression, in which case the hypothesis that the L1.X coefficient is 0 cannot be rejected? Furthermore, where can I learn more about how these probabilities are calculated? In my experience, most linear regression texts emphasis the hypothesis testing quite a bit, but I don't see any such sections when I look in time series books. What am I missing?
